Creating the Minecraft End Portal in Blender
In Cycles you may achieve this cool effect creating two different Scenes and combining them in compositor using the Alpha Over node (with a Holdout shader as a mask).


First check the Transparent checkbox in the Film panel of the Render header.


Create a plane and place it so it fits the door's jamb. Give it a Holdout shader. It will be used as a mask for mixing the two scenes in one render.


Create a new Scene (press the + button in the very top header), then choose New.


Now you have two scenes. You may switch between them as pictured below. Build two different worlds in each one. Your Camera and door object with holdout plane should be in the first Scene.
NOTE: Remember to change all the settings (such as render engine type, render settings etc.) for the nelwly created scene, so it fits the previous one.


Now select the Camera and door object, press Ctrl+L-->Objects to Scene and choose the second Scene (Scene.001). Objects origins should change their colors to blue- it means they're linked. Now you got them present in both scenes.


Now being in the first Scene go to the Node Editor (compositing nodes), add two Render Layers nodes, choose different scene for each one, render each scene (press the camera icon) and finally mix them using Alpha Over node (Add-->Color-->Alpha Over).


Open the Uv Editor in separate window and render (F12) being in the first Scene . Thanks to Alpha Over node your 'magic portal' is ready.





BONUS: To 'pass through' the other side of the portal you have to animate the Alpha Over node's Factor value. Keyframe it (I) with value 1.000 at the start of your animation, then go to the point when your camera 'doesn't see', what's on the other side of the portal and keyframe it again. Now go to the next frame (where your camera is behind the holdout plane), change the Fac value to 0.000 and keyframe it. After rendering you'll be on the other side :).